AutoSamplingTheory.SALD.cycle43LsiKlFiUpperObligation

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.ProofObligation. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def cycle43LsiKlFiUpperObligation : ProofObligation

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

This Lean definition constructs provenance or workflow data. It does not prove the mathematical statements stored as text. Status labels, named dependencies and citations are data, not compilation, proof or source certificates.

id : String (explicit)

Stable obligation identifier.

sald.lsi_kl_fi.cycle43_upper_packet

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Maintain the cycle 43 upper packet for main_body.tex lines 202-215: after cycle 41 Gronwall endpoint-safe progress and cycle 42 Donsker-Varadhan selected-test progress, select proof-closure item (3), eq:LSI-KL-FI, and direct middle/lower work toward the remaining Radon-Nikodym normalization, entropy integral transport, admissibility/approximation, zero-density, and vector/integral Fisher-chain interfaces for phi=sqrt(rho/pi), while keeping the full LSI-to-KL/FI theorem as an obligation until the analytic density-test backend builds.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldKlFiLsiSource — audited data reference, not expanded and not a compiled dependency edge

status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

1. SALD.cycle43LsiKlFiUpperPacket
2. SALD.lsiKlFiVocabularyContract
3. SALD.saldLsiKlFiDensityTestContract
4. SALD.lsiKlFiDensityTestObligation
5. SALD.cycle29LsiKlFiDensityTestMiddleObligation
6. SALD.cycle29LsiKlFiDensityTestLowerObligation
7. SALD.cycle33LsiKlFiDensityTestMiddleObligation
8. SALD.cycle33LsiKlFiDensityTestLowerObligation
9. SALD.cycle38LsiKlFiUpperObligation
10. SALD.cycle38LsiKlFiMiddleObligation
11. SALD.cycle38LsiKlFiLowerObligation
12. AutoSamplingTheory.lsiKlFiSqrtDensitySquareScalar
13. AutoSamplingTheory.lsiKlFiSqrtDensityEntropyIntegrandScalar
14. AutoSamplingTheory.lsiKlFiSqrtDensityNormalizationScalar
15. AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainScalar
16. AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainOfDerivativesScalar
17. AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainFiniteSumScalar
18. AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainFiniteSumHandoffScalar
19. AutoSamplingTheory.lsiKlFiRnDerivLIntegralMassOne
20. AutoSamplingTheory.lsiKlFiRnDerivDensityMassOne
21. AutoSamplingTheory.lsiKlFiSqrtRnDerivTestMassOne
22. AutoSamplingTheory.lsiKlFiRnDerivEntropyIntegral
23. AutoSamplingTheory.lsiKlFiSqrtRnDerivEntropyIntegral
24. SALD.lsiKlFiCoefficientAuditScalar
25. SALD.lsiKlFiDensityTestBridgeScalar
26. SALD.lsiKlFiHalfFisherScalar
27. SALD.lsiKlFiDensityTestHalfFisherScalar
28. probability.lsi_to_kl_fi

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

This is an upper-role assignment packet, not a proof of LSI-to-KL/FI. Lower work should try one proof-producing density/test-function backend lemma first and otherwise record a precise source-cited interface; eq:LSI-KL-FI remains an obligation.

def cycle43LsiKlFiUpperObligation : ProofObligation where
  id := "sald.lsi_kl_fi.cycle43_upper_packet"
  statement := "Maintain the cycle 43 upper packet for main_body.tex lines 202-215: after cycle 41 Gronwall endpoint-safe progress and cycle 42 Donsker-Varadhan selected-test progress, select proof-closure item (3), eq:LSI-KL-FI, and direct middle/lower work toward the remaining Radon-Nikodym normalization, entropy integral transport, admissibility/approximation, zero-density, and vector/integral Fisher-chain interfaces for phi=sqrt(rho/pi), while keeping the full LSI-to-KL/FI theorem as an obligation until the analytic density-test backend builds."
  source := saldKlFiLsiSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle43LsiKlFiUpperPacket",
    "SALD.lsiKlFiVocabularyContract",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.lsiKlFiDensityTestObligation",
    "SALD.cycle29LsiKlFiDensityTestMiddleObligation",
    "SALD.cycle29LsiKlFiDensityTestLowerObligation",
    "SALD.cycle33LsiKlFiDensityTestMiddleObligation",
    "SALD.cycle33LsiKlFiDensityTestLowerObligation",
    "SALD.cycle38LsiKlFiUpperObligation",
    "SALD.cycle38LsiKlFiMiddleObligation",
    "SALD.cycle38LsiKlFiLowerObligation",
    "AutoSamplingTheory.lsiKlFiSqrtDensitySquareScalar",
    "AutoSamplingTheory.lsiKlFiSqrtDensityEntropyIntegrandScalar",
    "AutoSamplingTheory.lsiKlFiSqrtDensityNormalizationScalar",
    "AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainScalar",
    "AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainOfDerivativesScalar",
    "AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainFiniteSumScalar",
    "AutoSamplingTheory.lsiKlFiSqrtDensityFisherChainFiniteSumHandoffScalar",
    "AutoSamplingTheory.lsiKlFiRnDerivLIntegralMassOne",
    "AutoSamplingTheory.lsiKlFiRnDerivDensityMassOne",
    "AutoSamplingTheory.lsiKlFiSqrtRnDerivTestMassOne",
    "AutoSamplingTheory.lsiKlFiRnDerivEntropyIntegral",
    "AutoSamplingTheory.lsiKlFiSqrtRnDerivEntropyIntegral",
    "SALD.lsiKlFiCoefficientAuditScalar",
    "SALD.lsiKlFiDensityTestBridgeScalar",
    "SALD.lsiKlFiHalfFisherScalar",
    "SALD.lsiKlFiDensityTestHalfFisherScalar",
    "probability.lsi_to_kl_fi"
  ]
  note := "This is an upper-role assignment packet, not a proof of LSI-to-KL/FI. Lower work should try one proof-producing density/test-function backend lemma first and otherwise record a precise source-cited interface; eq:LSI-KL-FI remains an obligation."

/-- Cycle-43 middle density-normalization and entropy-transport obligation.

The accompanying declarations in `AutoSamplingTheory/Probability.lean`
formalize the Mathlib-backed Radon-Nikodym mass and entropy transport pieces
for the source substitution `phi=sqrt(rho/pi)`.  The remaining Sobolev
admissibility and Fisher-chain integral theorem are still obligations.
-/